Capacity planning for batch and perfusion bioprocesses across multiple biopharmaceutical facilities

Production planning for biopharmaceutical portfolios becomes more complex when products switch between fed‐batch and continuous perfusion culture processes. This article describes the development of a discrete‐time mixed integer linear programming (MILP) model to optimize capacity plans for multiple biopharmaceutical products, with either batch or perfusion bioprocesses, across multiple facilities to meet quarterly demands. The model comprised specific features to account for products with fed‐batch or perfusion culture processes such as sequence‐dependent changeover times, continuous culture constraints, and decoupled upstream and downstream operations that permit independent scheduling of each. Strategic inventory levels were accounted for by applying cost penalties when they were not met. A rolling time horizon methodology was utilized in conjunction with the MILP model and was shown to obtain solutions with greater optimality in less computational time than the full‐scale model. The model was applied to an industrial case study to illustrate how the framework aids decisions regarding outsourcing capacity to third party manufacturers or building new facilities. The impact of variations on key parameters such as demand or titres on the optimal production plans and costs was captured. The analysis identified the critical ratio of in‐house to contract manufacturing organization (CMO) manufacturing costs that led the optimization results to favor building a future facility over using a CMO. The tool predicted that if titres were higher than expected then the optimal solution would allocate more production to in‐house facilities, where manufacturing costs were lower. Utilization graphs indicated when capacity expansion should be considered. © 2013 The Authors Biotechnology Progress published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 30:594–606, 2014     

Designing cost‐effective biopharmaceutical facilities using mixed‐integer optimization

Chromatography operations are identified as critical steps in a monoclonal antibody (mAb) purification process and can represent a significant proportion of the purification material costs. This becomes even more critical with increasing product titers that result in higher mass loads onto chromatography columns, potentially causing capacity bottlenecks. In this work, a mixed‐integer nonlinear programming (MINLP) model was created and applied to an industrially relevant case study to optimize the design of a facility by determining the most cost‐effective chromatography equipment sizing strategies for the production of mAbs. Furthermore, the model was extended to evaluate the ability of a fixed facility to cope with higher product titers up to 15 g/L. Examination of the characteristics of the optimal chromatography sizing strategies across different titer values enabled the identification of the maximum titer that the facility could handle using a sequence of single column chromatography steps as well as multi‐column steps. The critical titer levels for different ratios of upstream to dowstream trains where multiple parallel columns per step resulted in the removal of facility bottlenecks were identified. Different facility configurations in terms of number of upstream trains were considered and the trade‐off between their cost and ability to handle higher titers was analyzed. The case study insights demonstrate that the proposed modeling approach, combining MINLP models with visualization tools, is a valuable decision‐support tool for the design of cost‐effective facility configurations and to aid facility fit decisions. © 2013 The Authors. Published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 29:1472–1483, 2013     

Cybernetic modeling of the cephalosporin C fermentation process by Cephalosporium acremonium

A cybernetic mathematical model has been developed to describe the production of cephalosporin C. In developing the model, diauxic behavior of substrate consumption, morphological differentiation of cells, and catabolite repression of cephalosporin C production by the preferred substrate, glucose, were considered. The proposed model was tested on the experimental data from the literature and could adequately describe the morphological differentiation of cells, the sequential utilization of carbon sources and the production of cephalosporin C. It could be a useful tool to optimize the production of cephalosporin C by Cephalosporium acremonium in batch, fed-batch or continuous operations.     

Trichloroethene and cis‐1,2‐dichloroethene concentration‐dependent toxicity model simulates anaerobic dechlorination at high concentrations: I. batch‐fed reactors

A model was developed to describe toxicity from high concentrations of chlorinated aliphatic hydrocarbons (CAHs) on reductively dechlorinating cultures under batch‐growth conditions. A reductively dechlorinating anaerobic Evanite subculture (EV‐cDCE) was fed trichloroethene (TCE) and excess electron donor to accumulate cis‐1,2‐dichloroethene (cDCE) in batch‐fed reactors. A second Point Mugu (PM) culture was also studied in the cDCE accumulating batch‐fed experiment, as well as in a time‐ and concentration‐dependent cDCE exposure experiment. Both cultures accumulated cDCE to concentrations ranging from 9,000 to 12,000 µM before cDCE production from TCE ceased. Exposure to approximately 3,000 and 6,000 µM cDCE concentrations for 5 days during continuous TCE dechlorination exhibited greater loss in activity proportional to both time and concentration of exposure than simple endogenous decay. Various inhibition models were analyzed for the two cultures, including the previously proposed Haldane inhibition model and a maximum threshold inhibition model, but neither adequately fit all experimental observations. A concentration‐dependent toxicity model is proposed, which simulated all the experimental observations well. The toxicity model incorporates CAH toxicity terms that directly increase the cell decay coefficient in proportion with CAH concentrations. We also consider previously proposed models relating toxicity to partitioning in the cell wall (K_M/B), proportional to octanol–water partitioning (K_OW) coefficients. A reanalysis of previously reported modeling of batch tests using the Haldane model of Yu and Semprini, could be fit equally well using the toxicity model presented here, combined with toxicity proportioned to cell wall partitioning. A companion paper extends the experimental analysis and our modeling approach to a completely mixed reactor and a fixed film reactor. Biotechnol. Bioeng. 2010;107: 529–539. © 2010 Wiley Periodicals, Inc.     

Design of experiments applications in bioprocessing: Concepts and approach

Most biotechnology unit operations are complex in nature with numerous process variables, feed material attributes, and raw material attributes that can have significant impact on the performance of the process. Design of experiments (DOE)‐based approach offers a solution to this conundrum and allows for an efficient estimation of the main effects and the interactions with minimal number of experiments. Numerous publications illustrate application of DOE towards development of different bioprocessing unit operations. However, a systematic approach for evaluation of the different DOE designs and for choosing the optimal design for a given application has not been published yet. Through this work we have compared the I‐optimal and D‐optimal designs to the commonly used central composite and Box–Behnken designs for bioprocess applications. A systematic methodology is proposed for construction of the model and for precise prediction of the responses for the three case studies involving some of the commonly used unit operations in downstream processing. Use of Akaike information criterion for model selection has been examined and found to be suitable for the applications under consideration. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 30:86–99, 2014     

Controlling the time evolution of mAb N‐linked glycosylation ‐ Part II: Model‐based predictions

N‐linked glycosylation is known to be a crucial factor for the therapeutic efficacy and safety of monoclonal antibodies (mAbs) and many other glycoproteins. The nontemplate process of glycosylation is influenced by external factors which have to be tightly controlled during the manufacturing process. In order to describe and predict mAb N‐linked glycosylation patterns in a CHO‐S cell fed‐batch process, an existing dynamic mathematical model has been refined and coupled to an unstructured metabolic model. High‐throughput cell culture experiments carried out in miniaturized bioreactors in combination with intracellular measurements of nucleotide sugars were used to tune the parameter configuration of the coupled models as a function of extracellular pH, manganese and galactose addition. The proposed modeling framework is able to predict the time evolution of N‐linked glycosylation patterns during a fed‐batch process as a function of time as well as the manipulated variables. A constant and varying mAb N‐linked glycosylation pattern throughout the culture were chosen to demonstrate the predictive capability of the modeling framework, which is able to quantify the interconnected influence of media components and cell culture conditions. Such a model‐based evaluation of feeding regimes using high‐throughput tools and mathematical models gives rise to a more rational way to control and design cell culture processes with defined glycosylation patterns. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1135–1148, 2016     

Multivariate statistical monitoring as applied to clean‐in‐place (CIP) and steam‐in‐place (SIP) operations in biopharmaceutical manufacturing

Multivariate statistical process monitoring (MSPM) is becoming increasingly utilized to further enhance process monitoring in the biopharmaceutical industry. MSPM can play a critical role when there are many measurements and these measurements are highly correlated, as is typical for many biopharmaceutical operations. Specifically, for processes such as cleaning‐in‐place (CIP) and steaming‐in‐place (SIP, also known as sterilization‐in‐place), control systems typically oversee the execution of the cycles, and verification of the outcome is based on offline assays. These offline assays add to delays and corrective actions may require additional setup times. Moreover, this conventional approach does not take interactive effects of process variables into account and cycle optimization opportunities as well as salient trends in the process may be missed. Therefore, more proactive and holistic online continued verification approaches are desirable. This article demonstrates the application of real‐time MSPM to processes such as CIP and SIP with industrial examples. The proposed approach has significant potential for facilitating enhanced continuous verification, improved process understanding, abnormal situation detection, and predictive monitoring, as applied to CIP and SIP operations. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:505–515, 2014     

A dynamic metabolic flux balance based model of fed‐batch fermentation of bordetella pertussis

A mathematical model based on a dynamic metabolic flux balance (DMFB) is developed for a process of fed‐batch fermentation of Bordetella pertussis. The model is based on the maximization of growth rate at each time interval subject to stoichiometric constraints. The model is calibrated and verified with experimental data obtained in two different bioreactor experimental systems. It was found that the model calibration was mostly sensitive to the consumption or production rates of tyrosine and, for high supplementation rates, to the consumption rate of glutamate. Following this calibration the model correctly predicts biomass and by‐products concentrations for different supplementation rates. Comparisons of model predictions to oxygen uptake and carbon emission rates measurements indicate that the TCA cycle is fully functional. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29: 520–531, 2013     

Modeling the Residence Time Distribution of Integrated Continuous Bioprocesses

In response to the biopharmaceutical industry advancing from traditional batch operation to continuous operation, the Food and Drug Administration (FDA) has published a draft for continuous integrated biomanufacturing. This draft outlines the most important rules for establishing continuous integration. One of these rules is a thorough understanding of mass flows in the process. A computer simulation framework is developed for modeling the residence time distribution (RTD) of integrated continuous downstream processes based on a unit‐by‐unit modeling approach in which unit operations are simulated one‐by‐one across the entire processing time, and then combined into an integrated RTD model. The framework allows for easy addition or replacement of new unit operations, as well as quick adjustment of process parameters during evaluation of the RTD model. With this RTD model, the start‐up phase to reach steady state can be accelerated, the effects of process disturbances at any stage of the process can be calculated, and virtual tracking of a section of the inlet material throughout the process is possible. A hypothetical biomanufacturing process for an antibody was chosen for showcasing the RTD modeling approach.     

Continuous precipitation of process related impurities from clarified cell culture supernatant using a novel coiled flow inversion reactor (CFIR)

Coiled Flow Inverter Reactor (CFIR) has recently been explored for facilitating continuous operation of several unit operations involved in downstream processing of biopharmaceuticals such as viral inactivation and protein refolding. The application of CFIR for continuous precipitation of clarified cell culture supernatant has been explored. The pH based precipitation is optimized in the batch mode and then in the continuous mode in CFIR using a design of experiments (DOE) study. Improved clearance of host cell DNA (52× vs. 39× in batch), improved clearance of host cell proteins (HCP) (7× vs. 6× in batch) and comparable recovery (90 vs. 91.5 % in batch) are observed along with six times higher productivity. To further demonstrate wider applicability of CFIR in performing continuous precipitation, two more case studies involving use of two different precipitation protocols (CaCl₂ based and caprylic acid based) are also performed. In both cases, clearance of host cell DNA, HCP, and product recovery are found to be comparable or better in CFIR than in batch operations. Moreover, increase in productivity of 16 times (CaCl₂ based) and eight times (caprylic acid based) is obtained for the two precipitation protocols, respectively. The data clearly demonstrate that CFIR can be seamlessly integrated into a continuous bioprocess train for performing continuous precipitation of clarified cell culture supernatant. To our knowledge this is the first report of such use.     

Kinetic studies of the lactic acid fermentation in batch and continuous cultures

The fermentation kinetics of the homofermentative organism Lactobacillus delbrueckii in a glucose-yeast extract medium is studied in both batch and continuous culture under conditions of controlled pH. From a graphical analysis of the batch data, a mathematical model of the process is derived which relates bacterial growth, glucose utilization, and lactic acid formation. The parameters in the model represent the activity of the organism and are a function of pH, having a maximum value at about 5.90. In a continuous stirred tank fermentor (CSTF), the effect of pH, feed concentration, and residence time is observed. The feed medium is a constant ratio of two parts glucose to one part yeast extract plus added mineral salts. An approximate prediction of the steady-state behavior of the CSTF can be made using a method based on the kinetic model derived for the batch case. In making step changes from one steady state to another, the transient response is observed. Using the kinetic model to simulate the transient period, the calculated behavior qualitatively predicts the observed response.     

Equalizing growth in high‐throughput small scale cultivations via precultures operated in fed‐batch mode

An often underestimated problem when working with different clones in microtiter plates and shake flask screenings is the non‐parallel and non‐equal growth of batch cultures. These growth differences are caused by variances of individual clones regarding initial biomass concentration, lag‐phase or specific growth rate. Problems arising from unequal growth kinetics are different induction points in expression studies or uneven cultivation periods at the time of harvest. Screening for the best producing clones of a library under comparable conditions is thus often impractical or even impossible. A new approach to circumvent the problem of unequal growth kinetics of main cultures is the application of fed‐batch mode in precultures in microtiter plates and shake flasks. Fed‐batch operation in precultures is realized through a slow‐release system for glucose. After differently growing cultures turn to glucose‐limited growth, they all consume the same amount of glucose due to the fixed feed profile of glucose provided by the slow‐release system. This leads to equalized growth. Inherent advantages of this method are that it is easy to use and requires no additional equipment like pumps. This new technique for growth equalization in high‐throughput cultivations is simulated and verified experimentally. The growth of distinctly inoculated precultures in microtiter plates and shake flasks could be equalized for different microorganisms such as Escherichia coli and Hansenula polymorpha. Biotechnol. Bioeng. 2009;103: 1095–1102. © 2009 Wiley Periodicals, Inc.     

Model‐based optimization and pO2 control of fed‐batch Escherichia coli and Saccharomyces cerevisiae cultivation processes

A model‐based approach for optimization and cascade control of dissolved oxygen partial pressure (pO₂) and maximization of biomass in fed‐batch cultivations is presented. The procedure is based on the off‐line model‐based optimization of the optimal feeding rate profiles and the subsequent automatic pO₂ control using a proposed cascade control technique. During the model‐based optimization of the process, feeding rate profiles are optimized with respect to the imposed technological constraints (initial and maximal cultivation volume, cultivation time, feeding rate range, maximal oxygen transfer rate and pO₂ level). The cascade pO₂ control is implemented using activation of cascades for agitation, oxygen enrichment, and correction of the preoptimized feeding rate profiles. The proposed approach is investigated in two typical fed‐batch processes with Escherichia coli and Saccharomyces cerevisiae. The obtained results show that it was possible to achieve sufficiently high biomass levels with respect to the given technological constraints and to improve controllability of the investigated processes.     

Modeling of typical microbial cell growth in batch culture

A mathematical model was developed, based on the time dependent changes of the specific growth rate, for prediction of the typical microbial cell growth in batch cultures. This model could predict both the lag growth phase and the stationary growth phase of batch cultures, and it was tested with the batch growth ofTrichoderma reesei andLactobacillus delbrucckii.     

Predicting time to peak occurrence of insect life-stages usingregression models calibrated from stage-frequency data and ancillary stage-mortality data

1 Integrated Pest Management programmes often require predictions of peak occurrence of particular insect life‐stages to optimize the timing of population monitoring and control operations. 2 Given a known or estimated starting time for a synchronously developing pest population, predictive models estimated from stage‐frequency data alone can only predict the times of peak occurrence assuming a constant mortality rate across stages. 3 Here, continuation ratio regression models of relative stage frequencies estimated from stage‐frequency data are combined with a stage‐specific model of mortality estimated from ancillary mortality data to allow prediction of time of peak occurrence. 4 To calculate time of peak occurrence new mathematical derivations are given for continuation ratio models. 5 The models are used to predict the time of peak occurrence in degree‐day units for each of the first to third larval instars of the Tasmanian Eucalyptus leaf beetle Chrysophtharta bimaculata (Olivier) (Coleoptera: Chrysomelidae), a serious defoliator of Eucalyptus regnans and E. nitens plantations in Tasmania.     

Integration of stochastic simulation with multivariate analysis: Short‐term facility fit prediction

This article describes a decision‐support tool to help pinpoint the potential root causes of sub‐optimal short‐term facility fit issues in biopharmaceutical facilities. This was achieved by creating a tool that integrated stochastic simulation with advanced multivariate statistical analysis. Process fluctuations in product titers in cell culture, step yields, and chromatography eluate volumes were mimicked using Monte Carlo simulation data derived using a stochastic discrete‐event simulation model. The resulting stochastic datasets, with the computed consequences on key metrics such as product mass loss and cost of goods, were examined using advanced multivariate statistical techniques. Principal component analysis combined with clustering algorithms was used to analyze the complex datasets from complete industrial batch processes for biopharmaceuticals. The challenge of visualizing the multidimensional nature of the dataset was addressed using hierarchical and k‐means clustering as well as stacked parallel co‐ordinate plots to help identify process fingerprints and characteristics of clusters leading to sub‐optimal facility fit issues. Industrially‐relevant case studies are presented that focus on technology transfer challenges for therapeutic antibodies moving from early phase to late phase clinical trials. The case study details how sub‐optimal facility fit can be alleviated by allocating alternative product pool tanks. The impact of this operational change is then assessed by reviewing an updated process fingerprint. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29: 368–377, 2013     

A measure of explained variation for event history data

Summary There is no shortage of proposed measures of prognostic value of survival models in the statistical literature. They come under different names, including explained variation, correlation, explained randomness, and information gain, but their goal is common: to define something analogous to the coefficient of determination R² in linear regression. None however have been uniformly accepted, none have been extended to general event history data, including recurrent events, and many cannot incorporate time‐varying effects or covariates. We present here a measure specifically tailored for use with general dynamic event history regression models. The measure is applicable and interpretable in discrete or continuous time; with tied data or otherwise; with time‐varying, time‐fixed, or dynamic covariates; with time‐varying or time‐constant effects; with single or multiple event times; with parametric or semiparametric models; and under general independent censoring/observation. For single‐event survival data with neither censoring nor time dependency it reduces to the concordance index. We give expressions for its population value and the variance of the estimator and explore its use in simulations and applications. A web link to R software is provided.     

An artificial intelligence tool for bioprocess monitoring: application to continuous production of gluconic acid by immobilized Aspergillus niger

Experimental data on continuous fermentation of sucrose and glucose solution at low pH to gluconic acid by Asprgillus niger immobilized on cellulose fabric show complex dynamic behaviour including a decline in yield. The data have been analyzed using an artificial intelligence based symbolic regression technique to provide a mathematical model for predicting values of conversion 5, 10 and 15 h ahead values of conversion. These predictions can be used during continuous operations to monitor the bioprocess and adjust the residence time of fermentation to get complete and more efficient conversion of sucrose or glucose to gluconic acid.     

Cumulative Damage Survival Models for the Randomized Complete Block Design

A continuous time discrete state cumulative damage process {X(t), t ≥ 0} is considered, based on a non‐homogeneous Poisson hit‐count process and discrete distribution of damage per hit, which can be negative binomial, Neyman type A, Polya‐Aeppli or Lagrangian Poisson. Intensity functions considered for the Poisson process comprise a flexible three‐parameter family. The survival function is S(t) = P(X(t) ≤ L) where L is fixed. Individual variation is accounted for within the construction for the initial damage distribution {P(X(0) = x) | x = 0, 1, …,}. This distribution has an essential cut‐off before x = L and the distribution of L – X(0) may be considered a tolerance distribution. A multivariate extension appropriate for the randomized complete block design is developed by constructing dependence in the initial damage distributions. Our multivariate model is applied (via maximum likelihood) to litter‐matched tumorigenesis data for rats. The litter effect accounts for 5.9 percent of the variance of the individual effect. Cumulative damage hazard functions are compared to nonparametric hazard functions and to hazard functions obtained from the PVF‐Weibull frailty model. The cumulative damage model has greater dimensionality for interpretation compared to other models, owing principally to the intensity function part of the model.